timer Asked: Aug 9th, 2015

Question Description

Google Earth allows you to view many prominent buildings in 3d. Imagine that you are

the maths wiz at Google whose job it is to create a 3d image of our cube for Google Earth.

This means that you have to a nd coordinates of the corners of the square A;B;C;D visible

from the top, as well as the coordinates of the points A0;B0;C0;D0 at which four edges of

the Cube meet the ground. As indicated in the rst picture, A is supposed to be connected

to A0 by such an edge, and similarly for B and B0, C and C0, and D and D0.

You are new to this job and you are supposed to base your work on your predecessor's

work (who got fired yesterday). His notes are a terrible mess, but it is clear that he started

modelling the cube by letting the (

at) ground coincide with the xy-plane and having the

y-axis point West and the x-axis point North. His notes don't tell you where the origin of

his coordinate system is supposed to be, but wherever it may be, in this coordinate system

B = (26:3720; 35:3768; 13:1872), B0 = (24:9863; 31:7691; 0), D = (54:0957; 24:7282; 13:1872):

Your job also involves guring out how long the sides of the cube are; how long the four

segments AA0;BB0;CC0;DD0 are; how large the area of the quadrilateral A0;B0;C0;D0 is;

and, fi nally, what the volume of the part of the cube that sits above the ground is.

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